Spontaneous symmetry breaking in quantum many-body systems (A solid-state physicist’s view of Goldstone’s theorem and all that)

The concept of spontaneous symmetry breaking arose first in the context of superconductivity, before it became important for elementary particle physics. Starting with its original discovery, a comparison of the workings of the Goldstone mechanism in relativistic quantum fixed theory on the one hand and in quantum statistical mechanics on the other is given. The roles of locality and of long range forces are traced. For condensed matter physics, an approach using functional integral methods and macroscopic order parameter fields, valid near critical points is outlined. A possibly more widely valid approach is also presented, to complete this review of the Goldstone theories in quantum statistical mechanics. Talk delivered at the International Symposium on Theoretical Physics, Bangalore, November 1984.